PHY132_L16 - Classical Physics II Classical Physics II...

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lassical Physics II Classical Physics II PHY132 Lecture 17 Induction Lecture 16 1 03/08/2010
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Ampere’s Law the Biot-Savart Law (infinitesimally small current wire segment, or speeding charge) has a 1/ r 2 form, – it leads to a 1/ r form for the field of an infinitely long wire, nd o a constant field for a infinitely large “sheet” of current arrying wires – and to a constant field for a infinitely large sheet of current-carrying wires… This leads to a “geometric” interpretation of the field: field lines! The magnetic field lines always form closed loops – because of Gauss’ Law for magnetism, or the absence of magnetic monopoles … Above two observations results in AMPERE’S LAW, which (like Gauss’ Law for Electrostatics) is very useful for finding the B-field in symmetric situations. – Ampere’s Law is derivable as an ( line ) integral form of the Biot-Savart Law… Ampere’s Law: e n c l o s e d dI  Bs –wh e r e I enclosed is a current flowing through the surface enclosed by the curve, ore specifically: 0e closed curve Ampere's Law Lecture 16 2 more specifically: 03/08/2010 enclosed surface area bounded by the closed curve I d j A
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Applying Ampere’s Law Ampere’s Law is utilized by computer programs for field calculations. or ur purposes it is mostly useful in symmetric situations For our purposes it is mostly useful in symmetric situations – e.g. a long straight wire with current I (into the paper): – the B-field lines are circles around the wire: – Ampere’s Law applied to the dashed circle: B r I d Bs 2 B r 2 r B ds circle radius r 0e n c l o s e d 0 II  0 s we found before 0 2 I B r  Lecture 16 3 as we found before! 03/08/2010
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Magnetic Field from a Solenoid We’ll now use Ampere’s Law for other symmetric situations: The field of a very long solenoid: mpere’s Law applied to the Rectangular Amperian Loop l Ampere s Law applied to the dashed rectangle: •t h e B · d l vanishes for the left & right f fg sides because B is (nearly) perpendicular to these sides he B · d l vanishes for the top side because B is (nearly) zero there… hus: I N windings enclosed by the rectangle – Thus: rectangle d Bs 0 enclosed I 0 NI 0 eal solenoid NI B l  sol B l Lecture 16 4 03/08/2010 ideal solenoid
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